Such an apparatus is for instance known from NL1026527 of applicant. In the known apparatus, a tube film is inflated with the aid of an inflating unit, which provides the film with air via an air channel provided on one outer side of the film. On the same side of the film, a film conveying provision is provided on the apparatus for conveying the tube film and a sealing unit for sealing the inflated film tight. The tube film to be inflated is pretreated and comprises transversal seals and optionally transversal perforations for being able to tear off strings of air cushions. In use, the film is opened on the inflating side with the aid of a cutting element, and then air is blown therein and then the film is sealed tight again. A drawback of such an apparatus is that a film with a limited width can be processed thereon. Due to the fact that a certain minimum throughput rate is desired and a particular amount of air is needed for inflating the film, the width of the film is limited. When, in such an apparatus, the blow nozzle would be designed to blow in a larger amount of air per time unit, the air supply channel in the film should be wider. However, a wider air supply channel is undesired since it results in a larger edge of unused film on the inflated film. This is undesired for efficiency reasons. Therefore the known apparatus is not suitable for processing wide films for manufacturing mattress-like cushions, which are for instance used as exterior packaging for products in order to stabilize them in a further packaging and to protect them during transport.